Solve 1/36+1/45(24-x)

$$\frac { 1 } { 36 } + \frac { 1 } { 45 } ( 24 - x )$$

Evaluate

$$-\frac{x}{45}+\frac{101}{180}$$

Solution Steps

Use the distributive property to multiply \frac{1}{45} by 24-x.

$$\frac{1}{36}+\frac{1}{45}\times 24+\frac{1}{45}\left(-1\right)x$$

Multiply \frac{1}{45} and 24 to get \frac{24}{45}.

$$\frac{1}{36}+\frac{24}{45}+\frac{1}{45}\left(-1\right)x$$

Reduce the fraction \frac{24}{45} to lowest terms by extracting and canceling out 3.

$$\frac{1}{36}+\frac{8}{15}+\frac{1}{45}\left(-1\right)x$$

Multiply \frac{1}{45} and -1 to get -\frac{1}{45}.

$$\frac{1}{36}+\frac{8}{15}-\frac{1}{45}x$$

Least common multiple of 36 and 15 is 180. Convert \frac{1}{36} and \frac{8}{15} to fractions with denominator 180.

$$\frac{5}{180}+\frac{96}{180}-\frac{1}{45}x$$

Since \frac{5}{180} and \frac{96}{180} have the same denominator, add them by adding their numerators.

$$\frac{5+96}{180}-\frac{1}{45}x$$

Add 5 and 96 to get 101.

$$\frac{101}{180}-\frac{1}{45}x$$

Expand

$$-\frac{x}{45}+\frac{101}{180}$$

Solution Steps

Use the distributive property to multiply \frac{1}{45} by 24-x.

$$\frac{1}{36}+\frac{1}{45}\times 24+\frac{1}{45}\left(-1\right)x$$

Multiply \frac{1}{45} and 24 to get \frac{24}{45}.

$$\frac{1}{36}+\frac{24}{45}+\frac{1}{45}\left(-1\right)x$$

Reduce the fraction \frac{24}{45} to lowest terms by extracting and canceling out 3.

$$\frac{1}{36}+\frac{8}{15}+\frac{1}{45}\left(-1\right)x$$

Multiply \frac{1}{45} and -1 to get -\frac{1}{45}.

$$\frac{1}{36}+\frac{8}{15}-\frac{1}{45}x$$

Least common multiple of 36 and 15 is 180. Convert \frac{1}{36} and \frac{8}{15} to fractions with denominator 180.

$$\frac{5}{180}+\frac{96}{180}-\frac{1}{45}x$$

Since \frac{5}{180} and \frac{96}{180} have the same denominator, add them by adding their numerators.

$$\frac{5+96}{180}-\frac{1}{45}x$$

Add 5 and 96 to get 101.

$$\frac{101}{180}-\frac{1}{45}x$$